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# library for LMM
library(lme4)
library(lmerTest)
library(car)
Loading required package: carData
df<-read.csv("overall_scores.csv", header =TRUE, sep=",")
df
mod <- lm( novelty ~ factor(Group), data = df)
summary(mod)
Call:
lm(formula = novelty ~ factor(Group), data = df)
Residuals:
Min 1Q Median 3Q Max
-38.636 -29.894 -6.789 33.033 80.893
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.357 2.440 10.391 < 2e-16 ***
factor(Group)1 13.279 3.389 3.918 9.67e-05 ***
factor(Group)2 6.432 3.389 1.898 0.0581 .
factor(Group)3 4.537 3.409 1.331 0.1835
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 34.08 on 816 degrees of freedom
Multiple R-squared: 0.01925, Adjusted R-squared: 0.01564
F-statistic: 5.338 on 3 and 816 DF, p-value: 0.001207
mod <- lm(user.requirement ~ factor(Group) , data = df)
summary(mod)
Call:
lm(formula = user.requirement ~ factor(Group), data = df)
Residuals:
Min 1Q Median 3Q Max
-31.52 -20.51 -10.73 12.76 79.49
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.513 2.155 9.518 < 2e-16 ***
factor(Group)1 11.011 2.993 3.679 0.000249 ***
factor(Group)2 6.725 2.993 2.247 0.024902 *
factor(Group)3 10.219 3.010 3.395 0.000721 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 30.09 on 816 degrees of freedom
Multiple R-squared: 0.01998, Adjusted R-squared: 0.01637
F-statistic: 5.545 on 3 and 816 DF, p-value: 0.0009051
mod <- lm( infovis ~ factor(Group) , data = df)
summary(mod)
Call:
lm(formula = infovis ~ factor(Group), data = df)
Residuals:
Min 1Q Median 3Q Max
-38.631 -11.341 -3.011 13.659 59.402
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 28.098 1.502 18.711 < 2e-16 ***
factor(Group)1 10.533 2.085 5.051 5.44e-07 ***
factor(Group)2 5.969 2.085 2.862 0.00431 **
factor(Group)3 8.243 2.098 3.930 9.23e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 20.97 on 816 degrees of freedom
Multiple R-squared: 0.03314, Adjusted R-squared: 0.02958
F-statistic: 9.323 on 3 and 816 DF, p-value: 4.589e-06
mod <- lm( total ~ factor(Group) , data = df)
summary(mod)
Call:
lm(formula = total ~ factor(Group), data = df)
Residuals:
Min 1Q Median 3Q Max
-165.34 -68.06 -18.11 74.71 235.56
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 117.365 6.973 16.832 < 2e-16 ***
factor(Group)1 47.973 9.683 4.954 8.84e-07 ***
factor(Group)2 29.826 9.683 3.080 0.00214 **
factor(Group)3 38.626 9.740 3.966 7.96e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 97.37 on 816 degrees of freedom
Multiple R-squared: 0.03233, Adjusted R-squared: 0.02877
F-statistic: 9.086 on 3 and 816 DF, p-value: 6.39e-06
# convert to nominal factor
df$Group = factor(df$Group)
df$phase = factor(df$phase)
library(plyr)
ddply(df, ~ Group * phase, function(data) summary(data$novelty) )
ddply(df, ~ Group * phase, summarise, novelty.mean=mean(novelty), novelty.sd = sd(novelty))
# histograms for two factors
hist(df[df$Group == 0 & df$phase == 1,]$novelty)
hist(df[df$Group == 0 & df$phase == 2,]$novelty)
hist(df[df$Group == 0 & df$phase == 3,]$novelty)
hist(df[df$Group == 0 & df$phase == 4,]$novelty)
hist(df[df$Group == 1 & df$phase == 1,]$novelty)
hist(df[df$Group == 1 & df$phase == 2,]$novelty)
hist(df[df$Group == 1 & df$phase == 3,]$novelty)
hist(df[df$Group == 1 & df$phase == 4,]$novelty)
hist(df[df$Group == 2 & df$phase == 1,]$novelty)
hist(df[df$Group == 2 & df$phase == 2,]$novelty)
hist(df[df$Group == 2 & df$phase == 3,]$novelty)
hist(df[df$Group == 2 & df$phase == 4,]$novelty)
hist(df[df$Group == 3 & df$phase == 1,]$novelty)
hist(df[df$Group == 3 & df$phase == 2,]$novelty)
hist(df[df$Group == 3 & df$phase == 3,]$novelty)
hist(df[df$Group == 3 & df$phase == 4,]$novelty)
boxplot(novelty ~ Group * phase, data = df, xlab="Group.Phase", ylab="novelty")
with(df, interaction.plot(Group, phase, novelty, ylim=c(0, max(novelty)))) # interaction plot
m = lmer(novelty ~ Group + (1|Student), data=df, REML=FALSE)
summary(m)
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: novelty ~ Group + (1 | Student)
Data: df
AIC BIC logLik deviance df.resid
7866.7 7894.9 -3927.3 7854.7 814
Scaled residuals:
Min 1Q Median 3Q Max
-2.5709 -0.5208 -0.1870 0.6010 3.0064
Random effects:
Groups Name Variance Std.Dev.
Student (Intercept) 545.0 23.34
Residual 602.1 24.54
Number of obs: 820, groups: Student, 163
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 25.357 4.131 163.852 6.139 6.05e-09 ***
Group1 12.230 5.766 163.429 2.121 0.0354 *
Group2 6.432 5.736 163.852 1.121 0.2638
Group3 4.537 5.770 163.852 0.786 0.4328
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Group1 Group2
Group1 -0.716
Group2 -0.720 0.516
Group3 -0.716 0.513 0.516
plot(resid(m, type = "pearson") ~ fitted(m))
qqnorm(resid(m, type = "pearson"))
qqline(resid(m, type = "pearson"))
# library for LMM we will use on relational novelty
library(lme4)
library(lmerTest)
library(car)
contrasts(df$Group) <= "contr.sum"
1 2 3
0 TRUE TRUE TRUE
1 TRUE TRUE TRUE
2 TRUE TRUE TRUE
3 TRUE TRUE TRUE
contrasts(df$phase) <= "contr.sum"
2 3 4 5
1 TRUE TRUE TRUE TRUE
2 TRUE TRUE TRUE TRUE
3 TRUE TRUE TRUE TRUE
4 TRUE TRUE TRUE TRUE
5 TRUE TRUE TRUE TRUE
# phase is nested within group
fit <- lmer(novelty ~ ( Group / phase ) + ( 1 | Student), data = df, REML = FALSE)
Anova(fit, type=3, test.statistics="F")
Analysis of Deviance Table (Type III Wald chisquare tests)
Response: novelty
Chisq Df Pr(>Chisq)
(Intercept) 2.9277 1 0.08707 .
Group 7.1045 3 0.06864 .
Group:phase 118.9042 16 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
fit
Linear mixed model fit by maximum likelihood ['lmerModLmerTest']
Formula: novelty ~ (Group/phase) + (1 | Student)
Data: df
AIC BIC logLik deviance df.resid
7789.361 7892.966 -3872.681 7745.361 798
Random effects:
Groups Name Std.Dev.
Student (Intercept) 23.73
Residual 22.58
Number of obs: 820, groups: Student, 163
Fixed Effects:
(Intercept) Group1 Group2 Group3 Group0:phase2 Group1:phase2 Group2:phase2 Group3:phase2 Group0:phase3
8.974 17.914 15.728 10.893 13.141 7.609 7.440 3.150 18.109
Group1:phase3 Group2:phase3 Group3:phase3 Group0:phase4 Group1:phase4 Group2:phase4 Group3:phase4 Group0:phase5 Group1:phase5
14.157 5.555 5.437 20.513 11.771 4.340 10.722 30.150 19.861
Group2:phase5 Group3:phase5
18.095 30.823
library(multcomp)
Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS
Attaching package: ‘TH.data’
The following object is masked from ‘package:MASS’:
geyser
library(lsmeans)
Loading required package: emmeans
The 'lsmeans' package is now basically a front end for 'emmeans'.
Users are encouraged to switch the rest of the way.
See help('transition') for more information, including how to
convert old 'lsmeans' objects and scripts to work with 'emmeans'.
summary(glht(fit, lsm(pairwise ~ Group / phase)), test = adjusted(type='holm'))
NOTE: A nesting structure was detected in the fitted model:
phase %in% Group
Note: df set to 455
Simultaneous Tests for General Linear Hypotheses
Fit: lmer(formula = novelty ~ (Group/phase) + (1 | Student), data = df,
REML = FALSE)
Linear Hypotheses:
Estimate Std. Error t value Pr(>|t|)
phase1 Group0 - phase2 Group0 == 0 -13.1410 5.1137 -2.570 1.000000
phase1 Group0 - phase3 Group0 == 0 -18.1090 5.1137 -3.541 0.076425 .
phase1 Group0 - phase4 Group0 == 0 -20.5128 5.1137 -4.011 0.012630 *
phase1 Group0 - phase5 Group0 == 0 -30.1497 5.1137 -5.896 1.37e-06 ***
phase1 Group0 - phase1 Group1 == 0 -17.9138 7.3080 -2.451 1.000000
phase1 Group0 - phase2 Group1 == 0 -25.5228 7.3080 -3.492 0.090896 .
phase1 Group0 - phase3 Group1 == 0 -32.0704 7.3080 -4.388 0.002600 **
phase1 Group0 - phase4 Group1 == 0 -29.6845 7.3080 -4.062 0.010433 *
phase1 Group0 - phase5 Group1 == 0 -37.7750 7.3080 -5.169 6.57e-05 ***
phase1 Group0 - phase1 Group2 == 0 -15.7280 7.2838 -2.159 1.000000
phase1 Group0 - phase2 Group2 == 0 -23.1685 7.2838 -3.181 0.260457
phase1 Group0 - phase3 Group2 == 0 -21.2835 7.2838 -2.922 0.584132
phase1 Group0 - phase4 Group2 == 0 -20.0683 7.2838 -2.755 0.939603
phase1 Group0 - phase5 Group2 == 0 -33.8235 7.2838 -4.644 0.000825 ***
phase1 Group0 - phase1 Group3 == 0 -10.8934 7.3265 -1.487 1.000000
phase1 Group0 - phase2 Group3 == 0 -14.0439 7.3265 -1.917 1.000000
phase1 Group0 - phase3 Group3 == 0 -16.3305 7.3265 -2.229 1.000000
phase1 Group0 - phase4 Group3 == 0 -21.6152 7.3265 -2.950 0.540861
phase1 Group0 - phase5 Group3 == 0 -41.7166 7.3265 -5.694 4.19e-06 ***
phase2 Group0 - phase3 Group0 == 0 -4.9679 5.1137 -0.972 1.000000
phase2 Group0 - phase4 Group0 == 0 -7.3718 5.1137 -1.442 1.000000
phase2 Group0 - phase5 Group0 == 0 -17.0087 5.1137 -3.326 0.162779
phase2 Group0 - phase1 Group1 == 0 -4.7728 7.3080 -0.653 1.000000
phase2 Group0 - phase2 Group1 == 0 -12.3818 7.3080 -1.694 1.000000
phase2 Group0 - phase3 Group1 == 0 -18.9294 7.3080 -2.590 1.000000
phase2 Group0 - phase4 Group1 == 0 -16.5435 7.3080 -2.264 1.000000
phase2 Group0 - phase5 Group1 == 0 -24.6339 7.3080 -3.371 0.139903
phase2 Group0 - phase1 Group2 == 0 -2.5870 7.2838 -0.355 1.000000
phase2 Group0 - phase2 Group2 == 0 -10.0275 7.2838 -1.377 1.000000
phase2 Group0 - phase3 Group2 == 0 -8.1425 7.2838 -1.118 1.000000
phase2 Group0 - phase4 Group2 == 0 -6.9272 7.2838 -0.951 1.000000
phase2 Group0 - phase5 Group2 == 0 -20.6825 7.2838 -2.840 0.736765
phase2 Group0 - phase1 Group3 == 0 2.2476 7.3265 0.307 1.000000
phase2 Group0 - phase2 Group3 == 0 -0.9029 7.3265 -0.123 1.000000
phase2 Group0 - phase3 Group3 == 0 -3.1895 7.3265 -0.435 1.000000
phase2 Group0 - phase4 Group3 == 0 -8.4741 7.3265 -1.157 1.000000
phase2 Group0 - phase5 Group3 == 0 -28.5756 7.3265 -3.900 0.019679 *
phase3 Group0 - phase4 Group0 == 0 -2.4038 5.1137 -0.470 1.000000
phase3 Group0 - phase5 Group0 == 0 -12.0408 5.1137 -2.355 1.000000
phase3 Group0 - phase1 Group1 == 0 0.1952 7.3080 0.027 1.000000
phase3 Group0 - phase2 Group1 == 0 -7.4139 7.3080 -1.014 1.000000
phase3 Group0 - phase3 Group1 == 0 -13.9615 7.3080 -1.910 1.000000
phase3 Group0 - phase4 Group1 == 0 -11.5755 7.3080 -1.584 1.000000
phase3 Group0 - phase5 Group1 == 0 -19.6660 7.3080 -2.691 1.000000
phase3 Group0 - phase1 Group2 == 0 2.3810 7.2838 0.327 1.000000
phase3 Group0 - phase2 Group2 == 0 -5.0595 7.2838 -0.695 1.000000
phase3 Group0 - phase3 Group2 == 0 -3.1745 7.2838 -0.436 1.000000
phase3 Group0 - phase4 Group2 == 0 -1.9593 7.2838 -0.269 1.000000
phase3 Group0 - phase5 Group2 == 0 -15.7145 7.2838 -2.157 1.000000
phase3 Group0 - phase1 Group3 == 0 7.2155 7.3265 0.985 1.000000
phase3 Group0 - phase2 Group3 == 0 4.0650 7.3265 0.555 1.000000
phase3 Group0 - phase3 Group3 == 0 1.7785 7.3265 0.243 1.000000
phase3 Group0 - phase4 Group3 == 0 -3.5062 7.3265 -0.479 1.000000
phase3 Group0 - phase5 Group3 == 0 -23.6076 7.3265 -3.222 0.229024
phase4 Group0 - phase5 Group0 == 0 -9.6369 5.1137 -1.885 1.000000
phase4 Group0 - phase1 Group1 == 0 2.5990 7.3080 0.356 1.000000
phase4 Group0 - phase2 Group1 == 0 -5.0100 7.3080 -0.686 1.000000
phase4 Group0 - phase3 Group1 == 0 -11.5576 7.3080 -1.581 1.000000
phase4 Group0 - phase4 Group1 == 0 -9.1717 7.3080 -1.255 1.000000
phase4 Group0 - phase5 Group1 == 0 -17.2621 7.3080 -2.362 1.000000
phase4 Group0 - phase1 Group2 == 0 4.7848 7.2838 0.657 1.000000
phase4 Group0 - phase2 Group2 == 0 -2.6557 7.2838 -0.365 1.000000
phase4 Group0 - phase3 Group2 == 0 -0.7707 7.2838 -0.106 1.000000
phase4 Group0 - phase4 Group2 == 0 0.4446 7.2838 0.061 1.000000
phase4 Group0 - phase5 Group2 == 0 -13.3107 7.2838 -1.827 1.000000
phase4 Group0 - phase1 Group3 == 0 9.6194 7.3265 1.313 1.000000
phase4 Group0 - phase2 Group3 == 0 6.4689 7.3265 0.883 1.000000
phase4 Group0 - phase3 Group3 == 0 4.1823 7.3265 0.571 1.000000
phase4 Group0 - phase4 Group3 == 0 -1.1023 7.3265 -0.150 1.000000
phase4 Group0 - phase5 Group3 == 0 -21.2038 7.3265 -2.894 0.633576
phase5 Group0 - phase1 Group1 == 0 12.2360 7.3080 1.674 1.000000
phase5 Group0 - phase2 Group1 == 0 4.6269 7.3080 0.633 1.000000
phase5 Group0 - phase3 Group1 == 0 -1.9207 7.3080 -0.263 1.000000
phase5 Group0 - phase4 Group1 == 0 0.4653 7.3080 0.064 1.000000
phase5 Group0 - phase5 Group1 == 0 -7.6252 7.3080 -1.043 1.000000
phase5 Group0 - phase1 Group2 == 0 14.4217 7.2838 1.980 1.000000
phase5 Group0 - phase2 Group2 == 0 6.9812 7.2838 0.958 1.000000
phase5 Group0 - phase3 Group2 == 0 8.8662 7.2838 1.217 1.000000
phase5 Group0 - phase4 Group2 == 0 10.0815 7.2838 1.384 1.000000
phase5 Group0 - phase5 Group2 == 0 -3.6738 7.2838 -0.504 1.000000
phase5 Group0 - phase1 Group3 == 0 19.2563 7.3265 2.628 1.000000
phase5 Group0 - phase2 Group3 == 0 16.1058 7.3265 2.198 1.000000
phase5 Group0 - phase3 Group3 == 0 13.8192 7.3265 1.886 1.000000
phase5 Group0 - phase4 Group3 == 0 8.5346 7.3265 1.165 1.000000
phase5 Group0 - phase5 Group3 == 0 -11.5669 7.3265 -1.579 1.000000
phase1 Group1 - phase2 Group1 == 0 -7.6090 4.9276 -1.544 1.000000
phase1 Group1 - phase3 Group1 == 0 -14.1567 4.9276 -2.873 0.672665
phase1 Group1 - phase4 Group1 == 0 -11.7707 4.9276 -2.389 1.000000
phase1 Group1 - phase5 Group1 == 0 -19.8612 4.9276 -4.031 0.011805 *
phase1 Group1 - phase1 Group2 == 0 2.1858 7.1723 0.305 1.000000
phase1 Group1 - phase2 Group2 == 0 -5.2547 7.1723 -0.733 1.000000
phase1 Group1 - phase3 Group2 == 0 -3.3697 7.1723 -0.470 1.000000
phase1 Group1 - phase4 Group2 == 0 -2.1545 7.1723 -0.300 1.000000
phase1 Group1 - phase5 Group2 == 0 -15.9097 7.1723 -2.218 1.000000
phase1 Group1 - phase1 Group3 == 0 7.0203 7.2156 0.973 1.000000
phase1 Group1 - phase2 Group3 == 0 3.8698 7.2156 0.536 1.000000
phase1 Group1 - phase3 Group3 == 0 1.5833 7.2156 0.219 1.000000
phase1 Group1 - phase4 Group3 == 0 -3.7014 7.2156 -0.513 1.000000
phase1 Group1 - phase5 Group3 == 0 -23.8028 7.2156 -3.299 0.178036
phase2 Group1 - phase3 Group1 == 0 -6.5476 4.9276 -1.329 1.000000
phase2 Group1 - phase4 Group1 == 0 -4.1617 4.9276 -0.845 1.000000
phase2 Group1 - phase5 Group1 == 0 -12.2521 4.9276 -2.486 1.000000
phase2 Group1 - phase1 Group2 == 0 9.7948 7.1723 1.366 1.000000
phase2 Group1 - phase2 Group2 == 0 2.3543 7.1723 0.328 1.000000
phase2 Group1 - phase3 Group2 == 0 4.2393 7.1723 0.591 1.000000
phase2 Group1 - phase4 Group2 == 0 5.4546 7.1723 0.760 1.000000
phase2 Group1 - phase5 Group2 == 0 -8.3007 7.1723 -1.157 1.000000
phase2 Group1 - phase1 Group3 == 0 14.6294 7.2156 2.027 1.000000
phase2 Group1 - phase2 Group3 == 0 11.4789 7.2156 1.591 1.000000
phase2 Group1 - phase3 Group3 == 0 9.1923 7.2156 1.274 1.000000
phase2 Group1 - phase4 Group3 == 0 3.9077 7.2156 0.542 1.000000
phase2 Group1 - phase5 Group3 == 0 -16.1938 7.2156 -2.244 1.000000
phase3 Group1 - phase4 Group1 == 0 2.3860 4.9276 0.484 1.000000
phase3 Group1 - phase5 Group1 == 0 -5.7045 4.9276 -1.158 1.000000
phase3 Group1 - phase1 Group2 == 0 16.3424 7.1723 2.279 1.000000
phase3 Group1 - phase2 Group2 == 0 8.9019 7.1723 1.241 1.000000
phase3 Group1 - phase3 Group2 == 0 10.7869 7.1723 1.504 1.000000
phase3 Group1 - phase4 Group2 == 0 12.0022 7.1723 1.673 1.000000
phase3 Group1 - phase5 Group2 == 0 -1.7531 7.1723 -0.244 1.000000
phase3 Group1 - phase1 Group3 == 0 21.1770 7.2156 2.935 0.564420
phase3 Group1 - phase2 Group3 == 0 18.0265 7.2156 2.498 1.000000
phase3 Group1 - phase3 Group3 == 0 15.7399 7.2156 2.181 1.000000
phase3 Group1 - phase4 Group3 == 0 10.4553 7.2156 1.449 1.000000
phase3 Group1 - phase5 Group3 == 0 -9.6462 7.2156 -1.337 1.000000
phase4 Group1 - phase5 Group1 == 0 -8.0905 4.9276 -1.642 1.000000
phase4 Group1 - phase1 Group2 == 0 13.9565 7.1723 1.946 1.000000
phase4 Group1 - phase2 Group2 == 0 6.5160 7.1723 0.908 1.000000
phase4 Group1 - phase3 Group2 == 0 8.4010 7.1723 1.171 1.000000
phase4 Group1 - phase4 Group2 == 0 9.6162 7.1723 1.341 1.000000
phase4 Group1 - phase5 Group2 == 0 -4.1390 7.1723 -0.577 1.000000
phase4 Group1 - phase1 Group3 == 0 18.7910 7.2156 2.604 1.000000
phase4 Group1 - phase2 Group3 == 0 15.6406 7.2156 2.168 1.000000
phase4 Group1 - phase3 Group3 == 0 13.3540 7.2156 1.851 1.000000
phase4 Group1 - phase4 Group3 == 0 8.0693 7.2156 1.118 1.000000
phase4 Group1 - phase5 Group3 == 0 -12.0321 7.2156 -1.668 1.000000
phase5 Group1 - phase1 Group2 == 0 22.0469 7.1723 3.074 0.369591
phase5 Group1 - phase2 Group2 == 0 14.6065 7.1723 2.036 1.000000
phase5 Group1 - phase3 Group2 == 0 16.4915 7.1723 2.299 1.000000
phase5 Group1 - phase4 Group2 == 0 17.7067 7.1723 2.469 1.000000
phase5 Group1 - phase5 Group2 == 0 3.9515 7.1723 0.551 1.000000
phase5 Group1 - phase1 Group3 == 0 26.8815 7.2156 3.725 0.038848 *
phase5 Group1 - phase2 Group3 == 0 23.7310 7.2156 3.289 0.183214
phase5 Group1 - phase3 Group3 == 0 21.4444 7.2156 2.972 0.507933
phase5 Group1 - phase4 Group3 == 0 16.1598 7.2156 2.240 1.000000
phase5 Group1 - phase5 Group3 == 0 -3.9416 7.2156 -0.546 1.000000
phase1 Group2 - phase2 Group2 == 0 -7.4405 4.9276 -1.510 1.000000
phase1 Group2 - phase3 Group2 == 0 -5.5555 4.9276 -1.127 1.000000
phase1 Group2 - phase4 Group2 == 0 -4.3402 4.9276 -0.881 1.000000
phase1 Group2 - phase5 Group2 == 0 -18.0955 4.9276 -3.672 0.047345 *
phase1 Group2 - phase1 Group3 == 0 4.8346 7.1911 0.672 1.000000
phase1 Group2 - phase2 Group3 == 0 1.6841 7.1911 0.234 1.000000
phase1 Group2 - phase3 Group3 == 0 -0.6025 7.1911 -0.084 1.000000
phase1 Group2 - phase4 Group3 == 0 -5.8871 7.1911 -0.819 1.000000
phase1 Group2 - phase5 Group3 == 0 -25.9886 7.1911 -3.614 0.058656 .
phase2 Group2 - phase3 Group2 == 0 1.8850 4.9276 0.383 1.000000
phase2 Group2 - phase4 Group2 == 0 3.1002 4.9276 0.629 1.000000
phase2 Group2 - phase5 Group2 == 0 -10.6550 4.9276 -2.162 1.000000
phase2 Group2 - phase1 Group3 == 0 12.2751 7.1911 1.707 1.000000
phase2 Group2 - phase2 Group3 == 0 9.1246 7.1911 1.269 1.000000
phase2 Group2 - phase3 Group3 == 0 6.8380 7.1911 0.951 1.000000
phase2 Group2 - phase4 Group3 == 0 1.5533 7.1911 0.216 1.000000
phase2 Group2 - phase5 Group3 == 0 -18.5481 7.1911 -2.579 1.000000
phase3 Group2 - phase4 Group2 == 0 1.2152 4.9276 0.247 1.000000
phase3 Group2 - phase5 Group2 == 0 -12.5400 4.9276 -2.545 1.000000
phase3 Group2 - phase1 Group3 == 0 10.3901 7.1911 1.445 1.000000
phase3 Group2 - phase2 Group3 == 0 7.2396 7.1911 1.007 1.000000
phase3 Group2 - phase3 Group3 == 0 4.9530 7.1911 0.689 1.000000
phase3 Group2 - phase4 Group3 == 0 -0.3317 7.1911 -0.046 1.000000
phase3 Group2 - phase5 Group3 == 0 -20.4331 7.1911 -2.841 0.736765
phase4 Group2 - phase5 Group2 == 0 -13.7552 4.9276 -2.791 0.847574
phase4 Group2 - phase1 Group3 == 0 9.1748 7.1911 1.276 1.000000
phase4 Group2 - phase2 Group3 == 0 6.0243 7.1911 0.838 1.000000
phase4 Group2 - phase3 Group3 == 0 3.7377 7.1911 0.520 1.000000
phase4 Group2 - phase4 Group3 == 0 -1.5469 7.1911 -0.215 1.000000
phase4 Group2 - phase5 Group3 == 0 -21.6484 7.1911 -3.010 0.451634
phase5 Group2 - phase1 Group3 == 0 22.9301 7.1911 3.189 0.255168
phase5 Group2 - phase2 Group3 == 0 19.7796 7.1911 2.751 0.946564
phase5 Group2 - phase3 Group3 == 0 17.4930 7.1911 2.433 1.000000
phase5 Group2 - phase4 Group3 == 0 12.2083 7.1911 1.698 1.000000
phase5 Group2 - phase5 Group3 == 0 -7.8931 7.1911 -1.098 1.000000
phase1 Group3 - phase2 Group3 == 0 -3.1505 4.9874 -0.632 1.000000
phase1 Group3 - phase3 Group3 == 0 -5.4371 4.9874 -1.090 1.000000
phase1 Group3 - phase4 Group3 == 0 -10.7217 4.9874 -2.150 1.000000
phase1 Group3 - phase5 Group3 == 0 -30.8232 4.9874 -6.180 2.70e-07 ***
phase2 Group3 - phase3 Group3 == 0 -2.2866 4.9874 -0.458 1.000000
phase2 Group3 - phase4 Group3 == 0 -7.5712 4.9874 -1.518 1.000000
phase2 Group3 - phase5 Group3 == 0 -27.6727 4.9874 -5.549 9.16e-06 ***
phase3 Group3 - phase4 Group3 == 0 -5.2846 4.9874 -1.060 1.000000
phase3 Group3 - phase5 Group3 == 0 -25.3861 4.9874 -5.090 9.71e-05 ***
phase4 Group3 - phase5 Group3 == 0 -20.1015 4.9874 -4.030 0.011805 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- holm method)
fit.full <- lmer(novelty ~ ( Group / phase ) + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 + ( 1 | Student), data = df, REML = FALSE)
Anova(fit.full, type=3, test.statistics="F")
Analysis of Deviance Table (Type III Wald chisquare tests)
Response: novelty
Chisq Df Pr(>Chisq)
(Intercept) 1.0102 1 0.314852
Group 6.5217 3 0.088811 .
Q7_Q7_1 9.2241 1 0.002388 **
Q7_Q7_2 5.0628 1 0.024445 *
Q8_Q8_1 1.0258 1 0.311156
Q10 4.4038 1 0.035860 *
Group:phase 117.2473 16 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
fit.full
Linear mixed model fit by maximum likelihood ['lmerModLmerTest']
Formula: novelty ~ (Group/phase) + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 + (1 | Student)
Data: df
AIC BIC logLik deviance df.resid
7598.296 7720.096 -3773.148 7546.296 774
Random effects:
Groups Name Std.Dev.
Student (Intercept) 22.25
Residual 22.70
Number of obs: 800, groups: Student, 159
Fixed Effects:
(Intercept) Group1 Group2 Group3 Q7_Q7_1 Q7_Q7_2 Q8_Q8_1 Q10 Group0:phase2
-8.570 16.857 15.288 10.127 -4.858 3.739 1.701 5.196 13.851
Group1:phase2 Group2:phase2 Group3:phase2 Group0:phase3 Group1:phase3 Group2:phase3 Group3:phase3 Group0:phase4 Group1:phase4
7.795 6.402 3.150 19.088 14.502 5.691 5.437 21.622 12.058
Group2:phase4 Group3:phase4 Group0:phase5 Group1:phase5 Group2:phase5 Group3:phase5
4.446 10.722 30.158 20.346 18.537 30.823
# phase is nested within group
fit.requirement.full <- lmer(user.requirement ~ ( Group / phase ) + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 + ( 1 | Student), data = df, REML = FALSE)
Anova(fit.requirement.full, type=3, test.statistics="F")
Analysis of Deviance Table (Type III Wald chisquare tests)
Response: user.requirement
Chisq Df Pr(>Chisq)
(Intercept) 1.1511 1 0.28331
Group 2.6216 3 0.45371
Q7_Q7_1 6.1467 1 0.01317 *
Q7_Q7_2 3.2341 1 0.07212 .
Q8_Q8_1 0.9493 1 0.32990
Q10 5.4933 1 0.01909 *
Group:phase 164.9608 16 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
fit.requirement.full
Linear mixed model fit by maximum likelihood ['lmerModLmerTest']
Formula: user.requirement ~ (Group/phase) + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 + (1 | Student)
Data: df
AIC BIC logLik deviance df.resid
7335.734 7457.534 -3641.867 7283.734 774
Random effects:
Groups Name Std.Dev.
Student (Intercept) 20.70
Residual 18.91
Number of obs: 800, groups: Student, 159
Fixed Effects:
(Intercept) Group1 Group2 Group3 Q7_Q7_1 Q7_Q7_2 Q8_Q8_1 Q10 Group0:phase2
-8.258 9.712 5.259 8.142 -3.623 2.733 1.497 5.308 4.324
Group1:phase2 Group2:phase2 Group3:phase2 Group0:phase3 Group1:phase3 Group2:phase3 Group3:phase3 Group0:phase4 Group1:phase4
4.390 7.317 10.732 16.757 13.171 15.610 12.195 14.054 17.073
Group2:phase4 Group3:phase4 Group0:phase5 Group1:phase5 Group2:phase5 Group3:phase5
19.512 16.098 24.324 19.512 23.902 29.268
# histograms for two factors
boxplot(user.requirement ~ Group * phase, data = df, xlab="Group.Phase", ylab="user.requirement")
with(df, interaction.plot(Group, phase, user.requirement, ylim=c(0, max(user.requirement)))) # interaction plot
# phase is nested within group
fit.requirement <- lmer(user.requirement ~ ( Group / phase ) + ( 1 | Student), data = df, REML = FALSE)
Anova(fit, type=3, test.statistics="F")
Analysis of Deviance Table (Type III Wald chisquare tests)
Response: novelty
Chisq Df Pr(>Chisq)
(Intercept) 2.9277 1 0.08707 .
Group 7.1045 3 0.06864 .
Group:phase 118.9042 16 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
fit.requirement
Linear mixed model fit by maximum likelihood ['lmerModLmerTest']
Formula: user.requirement ~ (Group/phase) + (1 | Student)
Data: df
AIC BIC logLik deviance df.resid
7513.970 7617.574 -3734.985 7469.970 798
Random effects:
Groups Name Std.Dev.
Student (Intercept) 21.6
Residual 18.8
Number of obs: 820, groups: Student, 163
Fixed Effects:
(Intercept) Group1 Group2 Group3 Group0:phase2 Group1:phase2 Group2:phase2 Group3:phase2 Group0:phase3
8.718 11.137 5.568 8.355 4.615 4.286 7.143 10.732 15.897
Group1:phase3 Group2:phase3 Group3:phase3 Group0:phase4 Group1:phase4 Group2:phase4 Group3:phase4 Group0:phase5 Group1:phase5
12.857 15.238 12.195 14.359 16.667 19.048 16.098 24.103 19.048
Group2:phase5 Group3:phase5
23.333 29.268
plot(resid(m, type = "pearson") ~ fitted(m))
qqnorm(resid(m, type = "pearson"))
qqline(resid(m, type = "pearson"))
anova(fit.requirement, fit.requirement.full)
Error in anova.merMod(fit.requirement, fit.requirement.full) :
models were not all fitted to the same size of dataset